Finite Group Databasebeta

← C3×#10595191 #13174748

Subgroups — C3×#10595191 #13174748

Order 1728.

1254 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64147C211yesmaximal, characteristic
2C32×#936C211yesmaximal, characteristic, complemented
3C32×D4×Dic3C211yesmaximal, characteristic, complemented
4C3×#63975C212yesmaximal, complemented
5C3×#63956C212yesmaximal, complemented
6C3×#63955C212yesmaximal, complemented
7C3×#63952C212yesmaximal, complemented
8C3×C4×#624C211yesmaximal, characteristic, complemented
9C3×#63871C211yesmaximal, characteristic, complemented
10C3×#63869C211yesmaximal, characteristic, complemented
11C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
12C3×#5680—31nomaximal
13C3×#5557—31nomaximal
14#10595191C311yesmaximal, characteristic, direct product factor
15C2×C33×D4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C22×C32×Dic3C2212yes—
19C2×C32×Dic6C2211yescharacteristic
20C2×C3×#624C2211yescharacteristic
21C2×C3×#624C2211yescharacteristic
22C3×#3757C2212yes—
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C32×#217C2212yes—
25C32×#217C2212yes—
26C32×#217C2212yes—
27C32×C4⋊Dic3C2211yescharacteristic
28C32×C4×Dic3C2211yescharacteristic
29C32×C4×Dic3C2211yescharacteristic
30C3×#3724C2212yes—
31C3×Dic3⋊Dic3C2212yes—
32C3×Dic3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2212yes—
34C3×#3722C2212yes—
35C3×Dic32C2212yes—
36C3×Dic32C2211yescharacteristic
37C3×Dic32C2211yescharacteristic
38C32×#124—31no—
39C32×C4×D4—31no—
40#64147C2×C311yescharacteristic
41C3×#946—31no—
42C3×Q8×Dic3—31no—
43C3×#938—31no—
44C3×#938—31no—
45C3×#938—61no—
46C3×#936—21no—
47C3×#936D311yescharacteristic, complemented
48C3×#936C2×C311yescharacteristic, complemented
49C3×D4×Dic3—21no—
50C3×D4×Dic3D311yescharacteristic, complemented
51C3×D4×Dic3C2×C311yescharacteristic, complemented
52C3×C4×#67—32no—
53C3×#926—32no—
54C3×#897—31no—
55C3×#890—31no—
56C3×#883—32no—
57C3×#883—32no—
58C3×#67⋊C4—32no—
59C3×#879—32no—
60C3×#879—32no—
61C3×#877—32no—
62C3×C42×D3—31no—
63C3×C42×D3—31no—
64C3×#870—31no—
65C3×C4×Dic6—31no—
66#63975C2×C312yescomplemented
67#63956C2×C312yescomplemented
68#63955C2×C312yescomplemented
69#63952C2×C312yescomplemented
70C4×#624C2×C311yescharacteristic, complemented
71#63871C2×C311yescharacteristic, complemented
72#63869C2×C311yescharacteristic, complemented
73Dic3×Dic6C2×C311yescharacteristic, complemented
74C23×C33C2312yes—
75C22×C3×C3⋊D3C2311yescharacteristic
76C33×D4—22no—
77C2×C33×C4C2311yescharacteristic
78C3×#638—24no—
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C3×C4×C3⋊D3—22no—
82C2×C32×Dic3—24no—
83C2×C32×Dic3C2311yescharacteristic
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2312yes—
88C2×C32×Dic3C2311yescharacteristic
89C32×Dic6—22no—
90C3×#624—22no—
91C3×#624—22no—
92C3×#529—91no—
93#5680—31no—
94#5557—31no—
95C2×C32×Q8—31no—
96C2×C32×D4—21no—
97C2×C32×D4—21no—
98C2×C32×D4—21no—
99C2×C32×D4—41no—
100C2×C32×D4C2×D311yescharacteristic
101C2×C32×D4C2×D311yescharacteristic
102C2×C32×D4C22×C311yescharacteristic
103C22×C32×C4—32no—
104C2×#638C22×C312yes—
105C2×C4×C3⋊D3C22×C311yescharacteristic
106C2×C3×#67—32no—
107C2×C3×#67—32no—
108C2×C3×#67—62no—
109C22×C3×Dic3—22no—
110C22×C3×Dic3C2×D312yes—
111C22×C3×Dic3C22×C312yes—
112C2×C3×C4×D3—31no—
113C2×C3×C4×D3—31no—
114C2×C3×C4×D3—31no—
115C2×C3×C4×D3—31no—
116C2×C3×C4×D3—31no—
117C2×C3×C4×D3—31no—
118C2×C3×C4×D3—61no—
119C2×C3×Dic6—21no—
120C2×C3×Dic6C2×D311yescharacteristic
121C2×C3×Dic6C22×C311yescharacteristic
122C2×#624C22×C311yescharacteristic
123C2×#624C22×C311yescharacteristic
124C32×C4⋊C4—31no—
125C32×C22⋊C4—32no—
126C32×C22⋊C4—32no—
127C32×C22⋊C4—32no—
128C32×C42—31no—
129C32×C42—31no—
130#3757C22×C312yes—
131C4⋊(C3⋊Dic3)C22×C311yescharacteristic
132C3×#217—22no—
133C3×#217—22no—
134C3×#217—22no—
135C3×#217—32no—
136C3×#217—32no—
137C3×#217—62no—
138C3×#217C2×D312yes—
139C3×#217C2×D312yes—
140C3×#217C2×D312yes—
141C3×#217C22×C312yes—
142C3×#217C22×C312yes—
143C3×#217C22×C312yes—
144C3×(C2×D3)⋊C4—32no—
145C3×(C2×D3)⋊C4—32no—
146C3×C4⋊Dic3—21no—
147C3×C4⋊Dic3—31no—
148C3×C4⋊Dic3—31no—
149C3×C4⋊Dic3—32no—
150C3×C4⋊Dic3—32no—
151C3×C4⋊Dic3—32no—
152C3×C4⋊Dic3—61no—
153C3×C4⋊Dic3C2×D311yescharacteristic
154C3×C4⋊Dic3C22×C311yescharacteristic
155C3×Dic3⋊C4—32no—
156C3×Dic3⋊C4—32no—
157C3×Dic3⋊C4—32no—
158C3×Dic3⋊C4—32no—
159C3×Dic3⋊C4—32no—
160C3×C4×Dic3—21no—
161C3×C4×Dic3—21no—
162C3×C4×Dic3—31no—
163C3×C4×Dic3—32no—
164C3×C4×Dic3—31no—
165C3×C4×Dic3—31no—
166C3×C4×Dic3—31no—
167C3×C4×Dic3—32no—
168C3×C4×Dic3C2×D311yescharacteristic
169C3×C4×Dic3C2×D311yescharacteristic
170C3×C4×Dic3C22×C311yescharacteristic
171C3×C4×Dic3C22×C311yescharacteristic
172#3724C22×C312yes—
173Dic3⋊Dic3C22×C312yes—
174Dic3⋊Dic3C22×C312yes—
175Dic3⋊Dic3C22×C312yes—
176#3722C22×C312yes—
177Dic32C22×C312yes—
178Dic32C22×C311yescharacteristic
179Dic32C22×C311yescharacteristic
180C22×C33—22no—
181C22×C33—22no—
182C22×C33—22no—
183C22×C33C2411yescharacteristic
184C2×C3×C3⋊D3—21no—
185C2×C3×C3⋊D3—21no—
186C2×C3×C3⋊D3#4112yes—
187C33×C4#4112yes—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—22no—
190C32×Dic3—21no—
191C32×Dic3—21no—
192C32×Dic3—21no—
193C32×Dic3—22no—
194C32×Dic3—22no—
195C32×Dic3#4112yes—
196C3×#126—92no—
197C3×#125—91no—
198C3×#124—31no—
199C3×#124—31no—
200C3×#124—61no—
201C3×#123—92no—
202C3×C22⋊Q8—91no—
203C3×#121—91no—
204C3×C4×Q8—91no—
205C3×C4×D4—31no—
206C3×C4×D4—31no—
207C3×C4×D4—61no—
208C3×C4×D4—92no—
209C3×#117—92no—
210C2×C3×C42—91no—
211#946—31no—
212Q8×Dic3—31no—
213#938—31no—
214#938—31no—
215#938—61no—
216#936C3×D311yescharacteristic, complemented
217D4×Dic3C3×D311yescharacteristic, complemented
218C4×#67—32no—
219#926—32no—
220#897—31no—
221#890—31no—
222#883—32no—
223#883—32no—
224#67⋊C4—32no—
225#879—32no—
226#879—32no—
227#877—32no—
228C42×D3—31no—
229C42×D3—31no—
230#870—31no—
231C4×Dic6—31no—
232C23×C32—22no—
233C23×C32—22no—
234C23×C32—22no—
235C23×C32—42no—
236C23×C32C22×D312yes—
237C23×C32C22×D312yes—
238C23×C32C23×C312yes—
239C22×C3⋊D3C23×C311yescharacteristic
240C22×C3×D3—31no—
241C22×C3×D3—31no—
242C22×C3×D3—61no—
243C32×Q8—62no—
244C32×D4—22no—
245C32×D4—24no—
246C32×D4—22no—
247C32×D4—22no—
248C32×D4—42no—
249C32×D4—42no—
250C32×D4—44no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—31no—
255C2×C32×C4—31no—
256C2×C32×C4—31no—
257C2×C32×C4—31no—
258C2×C32×C4—32no—
259C2×C32×C4—32no—
260C2×C32×C4—41no—
261C2×C32×C4—64no—
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C23×C311yescharacteristic
265#638—24no—
266C2×C3⋊Dic3C23×C311yescharacteristic
267C2×C3⋊Dic3C23×C312yes—
268C4×C3⋊D3—22no—
269C3×#67—64no—
270C3×#67—64no—
271C3×#67—124no—
272C2×C3×Dic3—24no—
273C2×C3×Dic3—24no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—22no—
279C2×C3×Dic3—22no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—32no—
284C2×C3×Dic3—44no—
285C2×C3×Dic3—62no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3C22×D311yescharacteristic
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D311yescharacteristic
290C2×C3×Dic3C22×D312yes—
291C2×C3×Dic3C22×D312yes—
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C23×C312yes—
294C2×C3×Dic3C23×C311yescharacteristic
295C2×C3×Dic3C23×C311yescharacteristic
296C2×C3×Dic3C23×C311yescharacteristic
297C2×C3×Dic3C23×C312yes—
298C2×C3×Dic3C23×C311yescharacteristic
299C3×C4×D3—62no—
300C3×C4×D3—62no—
301C3×C4×D3—62no—
302C3×C4×D3—62no—
303C3×C4×D3—62no—
304C3×C4×D3—62no—
305C3×C4×D3—122no—
306C3×Dic6—22no—
307C3×Dic6—22no—
308C3×Dic6—42no—
309#624—22no—
310#624—22no—
311#529—91noSylow
312C2×C33—42no—
313C2×C33C2×#4111yescharacteristic
314C2×C33C2×#4111yescharacteristic
315C2×C33C2×#4111yescharacteristic
316C3×C3⋊D3—22no—
317C2×C3×Q8—31no—
318C2×C3×Q8—31no—
319C2×C3×Q8—61no—
320C2×C3×D4—21no—
321C2×C3×D4—21no—
322C2×C3×D4—21no—
323C2×C3×D4—41no—
324C2×C3×D4—92no—
325C2×C3×D4D3211yescharacteristic
326C2×C3×D4C2×C3×D311yescharacteristic
327C2×C3×D4C2×C3×D311yescharacteristic
328C22×C3×C4—32no—
329C22×C3×C4—32no—
330C22×C3×C4—62no—
331C22×C3×C4—91no—
332C22×C3×C4—91no—
333C22×C3×C4—91no—
334C2×#67—32no—
335C2×#67—32no—
336C2×#67—62no—
337C22×Dic3C2×C3×D312yes—
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—61no—
345C2×Dic6C2×C3×D311yescharacteristic
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—92no—
350C3×C4⋊C4—92no—
351C3×C4⋊C4—92no—
352C3×C4⋊C4—92no—
353C3×C4⋊C4—91no—
354C3×C22⋊C4—32no—
355C3×C22⋊C4—32no—
356C3×C22⋊C4—32no—
357C3×C22⋊C4—32no—
358C3×C22⋊C4—32no—
359C3×C22⋊C4—32no—
360C3×C22⋊C4—62no—
361C3×C22⋊C4—62no—
362C3×C22⋊C4—62no—
363C3×C22⋊C4—92no—
364C3×C22⋊C4—92no—
365C3×C42—31no—
366C3×C42—31no—
367C3×C42—31no—
368C3×C42—31no—
369C3×C42—61no—
370C3×C42—61no—
371C3×C42—91no—
372C3×C42—91no—
373C3×C42—92no—
374#217—32no—
375#217—32no—
376#217—62no—
377#217C2×C3×D312yes—
378#217C2×C3×D312yes—
379#217C2×C3×D312yes—
380(C2×D3)⋊C4—32no—
381(C2×D3)⋊C4—32no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—32no—
385C4⋊Dic3—32no—
386C4⋊Dic3—32no—
387C4⋊Dic3—61no—
388C4⋊Dic3C2×C3×D311yescharacteristic
389Dic3⋊C4—32no—
390Dic3⋊C4—32no—
391Dic3⋊C4—32no—
392Dic3⋊C4—32no—
393Dic3⋊C4—32no—
394C4×Dic3—32no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—32no—
400C4×Dic3C2×C3×D311yescharacteristic
401C4×Dic3C2×C3×D311yescharacteristic
402C22×C32—22no—
403C22×C32—24no—
404C22×C32—22no—
405C22×C32—22no—
406C22×C32—22no—
407C22×C32—22no—
408C22×C32—22no—
409C22×C32—22no—
410C22×C32—22no—
411C22×C32—22no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—41no—
416C22×C32—42no—
417C22×C32—42no—
418C22×C32—44no—
419C22×C32—42no—
420C22×C32—42no—
421C22×C32—42no—
422C22×C32—42no—
423C22×C32—42no—
424C22×C32—42no—
425C22×C32—82no—
426C22×C32—82no—
427C22×C32C23×D311yescharacteristic
428C22×C32C23×D311yescharacteristic
429C22×C32C24×C311yescharacteristic
430C2×C3⋊D3—21no—
431C2×C3⋊D3—21no—
432C2×C3⋊D3C3×#4112yes—
433C2×C3×D3—32no—
434C2×C3×D3—32no—
435C2×C3×D3—62no—
436C2×C3×D3—61no—
437C2×C3×D3—61no—
438C2×C3×D3—61no—
439C2×C3×D3—61no—
440C2×C3×D3—121no—
441C2×C3×D3—121no—
442C32×C4—22no—
443C32×C4—22no—
444C32×C4—22no—
445C32×C4—32no—
446C32×C4—42no—
447C32×C4—62no—
448C32×C4—61no—
449C32×C4—61no—
450C32×C4—61no—
451C32×C4—62no—
452C32×C4#23512yes—
453C32×C4#23712yes—
454C32×C4C3×#4112yes—
455C3⋊Dic3—21no—
456C3⋊Dic3—22no—
457C3×Dic3—22no—
458C3×Dic3—22no—
459C3×Dic3—21no—
460C3×Dic3—21no—
461C3×Dic3—21no—
462C3×Dic3—21no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—22no—
466C3×Dic3—22no—
467C3×Dic3—22no—
468C3×Dic3—42no—
469C3×Dic3—41no—
470C3×Dic3—41no—
471C3×Dic3—41no—
472C3×Dic3—42no—
473C3×Dic3—61no—
474C3×Dic3—61no—
475C3×Dic3—62no—
476C3×Dic3—62no—
477C3×Dic3—121no—
478C3×Dic3—122no—
479C3×Dic3#23712yes—
480C3×Dic3C3×#4112yes—
481#126—92no—
482#125—91no—
483#124—31no—
484#123—92no—
485C22⋊Q8—91no—
486#121—91no—
487C4×Q8—91no—
488C4×D4—31no—
489C4×D4—92no—
490#117—92no—
491C2×C42—91no—
492C33#52911yescharacteristic, complemented, Sylow
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—42no—
497C23×C3—91no—
498C23×C3C2×D3212yes—
499C23×C3C22×C3×D312yes—
500C23×C3C22×C3×D312yes—
501C22×D3—31no—
502C22×D3—31no—
503C22×D3—61no—
504C3×Q8—62no—
505C3×Q8—62no—
506C3×Q8—122no—
507C3×D4—24no—
508C3×D4—22no—
509C3×D4—22no—
510C3×D4—22no—
511C3×D4—42no—
512C3×D4—42no—
513C3×D4—44no—
514C3×D4—184no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—32no—
524C2×C3×C4—32no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—32no—
529C2×C3×C4—32no—
530C2×C3×C4—41no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—62no—
536C2×C3×C4—62no—
537C2×C3×C4—64no—
538C2×C3×C4—64no—
539C2×C3×C4—91no—
540C2×C3×C4—92no—
541C2×C3×C4—124no—
542C2×C3×C4—182no—
543C2×C3×C4—182no—
544C2×C3×C4—182no—
545C2×C3×C4C2×D3211yescharacteristic
546C2×C3×C4C22×C3×D311yescharacteristic
547C2×C3×C4C22×C3×D311yescharacteristic
548#67—64no—
549#67—64no—
550#67—124no—
551C2×Dic3—24no—
552C2×Dic3—31no—
553C2×Dic3—31no—
554C2×Dic3—32no—
555C2×Dic3—32no—
556C2×Dic3—62no—
557C2×Dic3—61no—
558C2×Dic3C22×C3×D311yescharacteristic
559C2×Dic3C22×C3×D311yescharacteristic
560C2×Dic3C22×C3×D311yescharacteristic
561C2×Dic3C22×C3×D312yes—
562C2×Dic3C22×C3×D312yes—
563C2×Dic3C22×C3×D311yescharacteristic
564C4×D3—62no—
565C4×D3—62no—
566C4×D3—62no—
567C4×D3—62no—
568C4×D3—62no—
569C4×D3—62no—
570C4×D3—122no—
571Dic6—22no—
572C2×C32—21no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—41no—
582C2×C32—41no—
583C2×C32—41no—
584C2×C32—42no—
585C2×C32—44no—
586C2×C32—42no—
587C2×C32—42no—
588C2×C32—82no—
589C2×C32—82no—
590C2×C32—84no—
591C2×C32C2×#23511yescharacteristic
592C2×C32C2×#23711yescharacteristic
593C2×C32C2×#23711yescharacteristic
594C2×C32D3×#4111yescharacteristic
595C2×C32D3×#4111yescharacteristic
596C2×C32D3×#4111yescharacteristic
597C2×C32C2×C3×#4111yescharacteristic
598C2×C32C2×C3×#4111yescharacteristic
599C2×C32C2×C3×#4111yescharacteristic
600C3⋊D3—22no—
601C3×D3—62no—
602C3×D3—62no—
603C3×D3—122no—
604C2×Q8—31no—
605C2×D4—92no—
606C2×D4C3×D3211yescharacteristic
607C22×C4—32no—
608C22×C4—91no—
609C22×C4—91no—
610C22×C4—91no—
611C4⋊C4—31no—
612C4⋊C4—92no—
613C4⋊C4—92no—
614C4⋊C4—92no—
615C4⋊C4—92no—
616C4⋊C4—91no—
617C22⋊C4—32no—
618C22⋊C4—32no—
619C22⋊C4—32no—
620C22⋊C4—92no—
621C22⋊C4—92no—
622C42—31no—
623C42—31no—
624C42—91no—
625C42—91no—
626C42—92no—
627C22×C3—24no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—22no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—42no—
641C22×C3—42no—
642C22×C3—42no—
643C22×C3—42no—
644C22×C3—42no—
645C22×C3—42no—
646C22×C3—42no—
647C22×C3—42no—
648C22×C3—44no—
649C22×C3—41no—
650C22×C3—82no—
651C22×C3—82no—
652C22×C3—92no—
653C22×C3—181no—
654C22×C3—181no—
655C22×C3C22×D3211yescharacteristic
656C22×C3C23×C3×D311yescharacteristic
657C22×C3C23×C3×D311yescharacteristic
658C2×D3—32no—
659C2×D3—32no—
660C2×D3—62no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—121no—
666C2×D3—121no—
667C3×C4—22no—
668C3×C4—22no—
669C3×C4—22no—
670C3×C4—32no—
671C3×C4—32no—
672C3×C4—42no—
673C3×C4—62no—
674C3×C4—62no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—62no—
679C3×C4—62no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—62no—
684C3×C4—122no—
685C3×C4—122no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—182no—
690C3×C4—181no—
691C3×C4#380412yes—
692C3×C4C3×#23512yes—
693C3×C4C3×#23712yes—
694Dic3—22no—
695Dic3—22no—
696Dic3—21no—
697Dic3—21no—
698Dic3—21no—
699Dic3—61no—
700Dic3—61no—
701Dic3—62no—
702Dic3—62no—
703Dic3—121no—
704Dic3—122no—
705Dic3C3×#23712yes—
706C32—21no—
707C32—21no—
708C32—21no—
709C32—41no—
710C32#555711yescharacteristic, complemented
711C32#568011yescharacteristic, complemented
712C32C3×#52911yescharacteristic, complemented
713C23—91no—
714C23C2×C3×D3212yes—
715Q8—62no—
716D4—22no—
717D4—184no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—32no—
723C2×C4—32no—
724C2×C4—64no—
725C2×C4—91no—
726C2×C4—92no—
727C2×C4—182no—
728C2×C4—182no—
729C2×C4—182no—
730C2×C4C2×C3×D3211yescharacteristic
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—44no—
741C2×C3—42no—
742C2×C3—42no—
743C2×C3—42no—
744C2×C3—41no—
745C2×C3—41no—
746C2×C3—41no—
747C2×C3—82no—
748C2×C3—82no—
749C2×C3—84no—
750C2×C3—182no—
751C2×C3D3×#23711yescharacteristic
752C2×C3#6431211yescharacteristic
753C2×C3C2×#380411yescharacteristic
754C2×C3C2×C3×#23511yescharacteristic
755C2×C3C2×C3×#23711yescharacteristic
756C2×C3C2×C3×#23711yescharacteristic
757C2×C3C3×D3×#4111yescharacteristic
758C2×C3C3×D3×#4111yescharacteristic
759C2×C3C3×D3×#4111yescharacteristic
760D3—62no—
761D3—62no—
762D3—122no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—92no—
767C22—181no—
768C22—181no—
769C22C22×C3×D3211yescharacteristic
770C4—32no—
771C4—62no—
772C4—62no—
773C4—61no—
774C4—61no—
775C4—61no—
776C4—181no—
777C4—182no—
778C4C3×#380412yes—
779C3—21no—
780C3—21no—
781C3—21no—
782C3—41no—
783C3#1059519111yescharacteristic, direct product factor
784C3C3×#555711yescharacteristic, complemented
785C3C3×#568011yescharacteristic, complemented
786C2—42no—
787C2—182no—
788C2C3×D3×#23711yescharacteristic
789C2C3×#6431211yescharacteristic
790C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
prime radicalC3×#64147C2
hypercenterC2×C3×D4D32
hypocenterC32C3×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C32×#936C2semidirect
3. C32×D4×Dic3C2semidirect
4. C3×#63975C2semidirect
5. C3×#63956C2semidirect
6. C3×#63955C2semidirect
7. C3×#63952C2semidirect
8. C3×C4×#624C2semidirect
9. C3×#63871C2semidirect
10. C3×#63869C2semidirect
11. C3×Dic3×Dic6C2semidirect
14. #10595191C3direct (N × H)
47. C3×#936D3semidirect
48. C3×#936C2×C3semidirect
50. C3×D4×Dic3D3semidirect
51. C3×D4×Dic3C2×C3semidirect
66. #63975C2×C3semidirect
67. #63956C2×C3semidirect
68. #63955C2×C3semidirect
69. #63952C2×C3semidirect
70. C4×#624C2×C3semidirect
71. #63871C2×C3semidirect
72. #63869C2×C3semidirect
73. Dic3×Dic6C2×C3semidirect
216. #936C3×D3semidirect
217. D4×Dic3C3×D3semidirect
492. C33#529semidirect
710. C32#5557semidirect
711. C32#5680semidirect
712. C32C3×#529semidirect
783. C3#10595191direct (N × H)
784. C3C3×#5557semidirect
785. C3C3×#5680semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#641472
C32×#9362
C32×D4×Dic32
C3×#639752
C3×#639562
C3×#639552
C3×#639522
C3×C4×#6242
C3×#638712
C3×#638692
C3×Dic3×Dic62
C3×#56803
C3×#55573
#105951913